Basic properties
| Modulus: | \(6776\) | |
| Conductor: | \(484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{484}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6776.ee
\(\chi_{6776}(127,\cdot)\) \(\chi_{6776}(183,\cdot)\) \(\chi_{6776}(519,\cdot)\) \(\chi_{6776}(743,\cdot)\) \(\chi_{6776}(799,\cdot)\) \(\chi_{6776}(855,\cdot)\) \(\chi_{6776}(1135,\cdot)\) \(\chi_{6776}(1359,\cdot)\) \(\chi_{6776}(1415,\cdot)\) \(\chi_{6776}(1471,\cdot)\) \(\chi_{6776}(1751,\cdot)\) \(\chi_{6776}(1975,\cdot)\) \(\chi_{6776}(2031,\cdot)\) \(\chi_{6776}(2087,\cdot)\) \(\chi_{6776}(2367,\cdot)\) \(\chi_{6776}(2591,\cdot)\) \(\chi_{6776}(2647,\cdot)\) \(\chi_{6776}(2703,\cdot)\) \(\chi_{6776}(2983,\cdot)\) \(\chi_{6776}(3207,\cdot)\) \(\chi_{6776}(3263,\cdot)\) \(\chi_{6776}(3319,\cdot)\) \(\chi_{6776}(3599,\cdot)\) \(\chi_{6776}(3823,\cdot)\) \(\chi_{6776}(3879,\cdot)\) \(\chi_{6776}(3935,\cdot)\) \(\chi_{6776}(4215,\cdot)\) \(\chi_{6776}(4439,\cdot)\) \(\chi_{6776}(4495,\cdot)\) \(\chi_{6776}(4551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1695,3389,969,3753)\) → \((-1,1,1,e\left(\frac{89}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 6776 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{1}{10}\right)\) |